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In this thesis we present contributions in the field of the applications of quantum field theories techniques to condensed matter models. In chapter 3 we investigate on the non covariant fermionic determinant and its connection to Luttinger…
A model with a singular forward scattering amplitude for particles with opposite spins in d spatial dimensions is proposed and solved by using the bosonization transformation. This interacting potential leads to the spin-charge separation.…
Spin liquids are novel states of matter with fractionalized excitations. A recent numerical study of Hubbard model on a honeycomb lattice\cite{Meng2010} indicates that a gapped spin liquid phase exists close to the Mott transition. Using…
Fermions in two-dimensions (2D) when subject to anisotropic spin-dependent hopping can potentially give rise to unusual paired states in {\it unpolarized} mixtures that can behave as non-Fermi liquids. One possibility is a fully paired…
The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization…
A two dimensional random hopping model with N-species and \pi-flux is studied. The field theory at the band center is shown to be in the universality class of GL(4m,R)/O(4m) nonlinear sigma model. Vanishing beta function suggests…
A scheme is proposed to construct integer and fractional topological quantum states of fermions in two spatial dimensions. We devise models for such states by coupling wires of non-chiral Luttinger liquids of electrons, that are arranged in…
We point to the possibility of existence of the statistical-spin-liquid state as the state which differs from either Fermi or Luttinger liquid states. In the statistical spin liquid the double occupancies are excluded from the physical…
The liquid-to-ordered phase transition in a bilayer system of fermions is studied within the context of a recently proposed density-functional theory [Phys. Rev. A {\bf 92}, 023614 (2015)]. In each two-dimensional layer, the fermions…
We study a one-dimensional system that consists of an electron gas coupled to a spin-1/2 chain by Kondo interaction away from half-filling. We show that zero-temperature transitions between phases with "small" and "large" Fermi momenta can…
On several one-dimensional (1D) and 2D nonbipartite lattices, we study both free and Hubbard interacting lattice fermions when some magnetic fluxes are threaded or gauge fields coupled. First, we focus on finding out the optimal flux which…
The model of local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems is studied for anisotropic pairing symmetry. The phase diagram is presented and the…
We investigate the stability of helical superfluid phase in a spin-orbit coupled Fermi gas loaded in a bilayer optical lattice. The phase diagram of the system is constructed in the mean field framework. We investigate the topological…
We study an exchange coupled system of itinerant electrons and localized fermion pairs resulting in a resonant pairing formation. This system inherently contains resonating fermion pairs on bonds which lead to a superconducting phase…
We study the repulsive Hubbard model on an anisotropic honeycomb lattice within a mean-field and a slave-rotor treatment. In addition to the known semi-metallic and band-insulating phases, obtained for very weak interactions, and the…
Band flattening has been identified as key ingredient to correlation phenomena in Moir\'e materials and beyond. Here, we examine strongly repulsive fermions on a ladder -- a minimal platform for unconventional $d$-wave pairing -- and show…
We study a two-component Fermi system with attractive interactions and different populations of the two species in a cubic lattice. For an intermediate coupling we find a uniformly polarized superfluid which is stable down to very low…
We study the dynamics of a heavy particle of mass $M$ moving in a one-dimensional repulsively interacting Fermi gas. The Fermi gas is described using the Luttinger model and bosonization. By transforming to a frame co-moving with the heavy…
We use higher-dimensional bosonization to study the normal state of electrons in weakly coupled metallic chains interacting with long-range Coulomb forces. Particular attention is paid to the crossover between Luttinger and Fermi liquid…
We calculate the correlation functions and the DC conductivity of Luttinger liquid superlattices, modeled by a repeated pattern of interacting and free Luttinger liquids. In a specific realization, where the interacting subsystem is a…